MF 803: Advanced Programming for Mathematical Finance
Mathematical Finance代写 Re-run your bootstrapping procedure with this new curve. Comment on the changes to the forward rates.
Problem set # 5 Mathematical Finance代写
Due: Wednesday, October 30th, by 6:30pm.
1. Yield Curve Construction:
Consider the following table of USD swap rates:
1Y 2.8438
2Y 3.060
3Y 3.126
4Y 3.144
5Y 3.150
7Y 3.169
10Y 3.210
30Y 3.237
Note: You may assume that these swaps pay coupons semi-annually (every 6 months). For simplicity, you may use a year fraction of 0.5 in all swap coupon payments. Mathematical Finance代写
(a)Extractthe constant forward rate for the first year that enables you to match the 1Y market swap rate.
(b)Holding this first year forward rate fixed, find the forward rate from one year to two yearsthat enables you to match the two year swap (while also matching the one year).
(c)Continuethis process and extract piecewise constant forward rates for the entire Comment on the forward rates vs. the swap rates.
(d)Compute the fair market, breakeven swap rate of a 15Y swap. That is, find the swap rate that equates the present values of the fixed and floating legs.
(e)Compute discount factors. Compute zero rates by finding the constant rate that leads to the calibrated discount factors. Comment on the differences in the zero rates and swap rates.
(f)Shiftall forward rates up 100 basis points and re-calculate the breakeven swap rates for each benchmark point. Mathematical Finance代写
Generate a table of new swap rates. Are these rates equivalent to having shifted the swap rates directly?
(g)Consider a bearish steepener to the swap rates, that is perform the following shifts on each swaprate:
1Y +0 bps
2Y +0 bps
3Y +0 bps
4Y +5 bps
5Y +10 bps
7Y +15 bps
10Y +25 bps
30Y +50 bps
Print the new swap rates.
(h)Re-run your bootstrapping procedure with this new curve. Comment on the changes to the forward rates.
(i)Considera bull steepener to the swap rates, that is perform the following shifts on each swap rate: Mathematical Finance代写
1Y -50 bps
2Y -25 bps
3Y -15 bps
4Y -10 bps
5Y -5 bps
7Y +0 bps
10Y +0 bps
30Y +0 bps
Print the new swap rates.
(j)Re-run your bootstrapping procedure with this new curve. Comment on the changes to the forward rates.
NOTE: All code for completing these exercises should be completed either in Python or C++ and should be written generically. You may end up using this code on future assignments so I encourage you to code thoughtfully.
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